Gradient evolution-based counter propagation network for approximation of noncanonical system

  • Uday Pratap Singh
  • Sanjeev Jain
  • Akhilesh Tiwari
  • Rajeev Kumar Singh
Methodologies and Application


In this paper, gradient evolution-based counter propagation network (GE-CPN) is developed for approximation of noncanonical form of nonlinear system and compared with some existing neural networks. GE-CPN is a multilayer feed-forward neural network, in which initial weights are assigning by the minimization of fitness function, i.e., mean-square error (MSE). An important feature of GE-CPN networks is learning from input data of nonlinear systems with parametric uncertainties. Under the framework of nonlinear system approximation using soft computing method, a new method GE-CPN is used to approximate the noncanonical systems. Adaptive and robust control of noncanonical systems in the presence of parameterization of system dynamics is much difficult. GE-CPN is used for approximation of noncanonical nonlinear systems at relative degree of accuracy. This paper shows that it is necessary to reparameterize neural network model and that such reparameterization is helpful for approximation of noncanonical systems. To demonstrate the effectiveness of GE-CPN method, simulation has been carried out by four noncanonical nonlinear systems.


Gradient evolution Noncanonical system Neural network Tracking error 


Compliance with ethical standards

Conflict of interest

On behalf of other author’s I declare that we have no conflict of interest.

Ethical approval

This article do not contain studies with human participants or animals by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Uday Pratap Singh
    • 1
  • Sanjeev Jain
    • 2
  • Akhilesh Tiwari
    • 3
  • Rajeev Kumar Singh
    • 3
  1. 1.Department of Applied MathematicsMadhav Institute of Technology and ScienceGwaliorIndia
  2. 2.Department of Computer Science & EngineeringShri Mata Vaishno Devi UniversityKatraIndia
  3. 3.Department of CSE & ITMadhav Institute of Technology and ScienceGwaliorIndia

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